CSE370 Quiz 1 (10 April) Solution
 
 

Write down the Boolean expression that corresponds to the following logic circuit. 

Z = [ (ABC)' (BC')' A ]' = ABC + BC' + A'
 Fill in the truth table for the function.
 
A
B
C
ABC
  BC' 
 A'
Z
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
 
Write the function above in canonical sum-of-products form. 
Z = A'B'C' + A'B'C + A'BC' + A'BC + ABC' + ABC
Simplify the function above using the axioms/theorems of Boolean algebra (show each step): 
Z = ABC + BC' + A'         Z = A'B'C' + A'B'C + A'BC' + A'BC + ABC' + ABC
  = B(AC + C') + A'          = A'(B'C' + B'C + BC' + BC) + AB(C' + C)
  = B(A + C') + A'           = A' + AB
  = AB + BC' + A'            = A' + B
  = A' + B + BC'
  = A' + B
Comments to: cse370-webmaster@cs.washington.edu (Last Update: )